Simplify the following expression: $z = \dfrac{y - 11}{y - 12} - \dfrac{9y - 19}{y - 12}$
Solution: Since the expressions have the same denominator we simply subtract the numerators: $z = \dfrac{y - 11 - (9y - 19)}{y - 12}$ Distribute the negative sign: $z = \dfrac{y - 11 - 9y + 19}{y - 12}$ Combine like terms: $z = \dfrac{-8y + 8}{y - 12}$